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Today we will begin our investigation of reflections. We want to know how reflecting a figure would affect the figure. To reflect an object just means to "flip" it across a line. (Hint: Think of the "fl" in the word reflection, it will remind you of the "fl" in the word flip.) For our purposes, we will stick to reflecting across either the x or y axis. (If you haven't watched the video on the previous post about plotting points, you should do so as a refresher on the basics of the coordinate plane.) The line you reflect across is called the line of reflection. Imagine folding a piece of paper along this line. The original image and the reflected image should match when the paper is folded on the line of reflection. To reflect an image, first identify the line of reflection (usually the x or y axis). Begin by reflecting each point individually. To do this, you would count the number of spaces between that point and the line of reflection. Move the same number of spaces on the other side of the line and you have your new point (remember these are marked as prime points (')). Do this for each point on the figure. Connect your points and you have a reflected image. To check your work, fold the paper along the line of reflection. Do your images match up?
NOw, what effect does the reflection have on the image? Does it change the size or shape? If the two images match when you fold the paper, the size and shape must be the same. You will remember from the previous lesson on translations that this means the shapes are congruent. Just like a translation, reflections lead to congruent figures.
Watch the video for more on how to reflect a figure in the coordinate plane.
NOw, what effect does the reflection have on the image? Does it change the size or shape? If the two images match when you fold the paper, the size and shape must be the same. You will remember from the previous lesson on translations that this means the shapes are congruent. Just like a translation, reflections lead to congruent figures.
Watch the video for more on how to reflect a figure in the coordinate plane.